Express this quotient in scientific notation: ${\frac{1.110\times 10^{-1}} {3.0\times 10^{1}}}$
Solution: Start by collecting like terms together. $= {\frac{1.110} {3.0}} \times{\frac{10^{-1}} {10^{1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.37 \times 10^{-1\,-\,1}$ $= 0.37 \times 10^{-2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.37$ is the same as $3.70 \div 10$ , or $3.70 \times 10^{-1}$ $ = {3.70 \times 10^{-1}} \times 10^{-2} $ $= 3.70\times 10^{-3}$